Problem: Solve for $x$ and $y$ using elimination. ${3x-2y = 16}$ ${-4x+2y = -26}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-x = -10$ $\dfrac{-x}{{-1}} = \dfrac{-10}{{-1}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {3x-2y = 16}\thinspace$ to find $y$ ${3}{(10)}{ - 2y = 16}$ $30-2y = 16$ $30{-30} - 2y = 16{-30}$ $-2y = -14$ $\dfrac{-2y}{{-2}} = \dfrac{-14}{{-2}}$ ${y = 7}$ You can also plug ${x = 10}$ into $\thinspace {-4x+2y = -26}\thinspace$ and get the same answer for $y$ : ${-4}{(10)}{ + 2y = -26}$ ${y = 7}$